There exist various central limit-type theorems in the literature pertaining to sums of eigenvalues of random matrices e.g. [1]}, [2]}, [3]}, [4]}. Among the earliest results in this direction are due to Johansson [2]}. These specific results concern random Hermitian matrices distributed according to the probability measure
\(d\mu _{n,\tau }(A) \propto \exp \big ( -\tau \operatorname{tr}V(A)\big )\,dA,\) 
